Finite Group Databasebeta

← C3×#10611916 #14424526

Subgroups — C3×#10611916 #14424526

Order 1920.

1400 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4147C211yesmaximal, characteristic
2C2×C3×#4064C211yesmaximal, characteristic, complemented
3C2×C3×D5×Q16C211yesmaximal, characteristic, complemented
4C3×#65962C211yesmaximal, characteristic, complemented
5C3×C5×#451C211yesmaximal, characteristic, complemented
6C3×#65517C211yesmaximal, characteristic, complemented
7C3×#65476C211yesmaximal, characteristic, complemented
8C3×#65475C211yesmaximal, characteristic, complemented
9C3×#65336C211yesmaximal, characteristic, complemented
10C3×#65099C211yesmaximal, characteristic, complemented
11C3×#65097C211yesmaximal, characteristic, complemented
12C3×#65093C211yesmaximal, characteristic, complemented
13C3×#65091C211yesmaximal, characteristic, complemented
14C3×#65022C211yesmaximal, characteristic, complemented
15C3×#65016C211yesmaximal, characteristic, complemented
16#10611916C311yesmaximal, characteristic, direct product factor, Hall
17C22×C3×C5×Q8C2211yescharacteristic
18C3×#4147—24no—
19C3×#4147—24no—
20C2×C3×#713—21no—
21C2×C3×#713C2211yescharacteristic
22C2×C3×#713C2211yescharacteristic
23C2×C3×Q8×D5—21no—
24C2×C3×Q8×D5C2211yescharacteristic
25C2×C3×Q8×D5C2211yescharacteristic
26C2×C3×Q8×D5C2211yescharacteristic
27C2×C3×#709—21no—
28C2×C3×#709—21no—
29C2×C3×#709C2211yescharacteristic
30C2×C3×#709C2211yescharacteristic
31C2×C3×C5×Q16C2211yescharacteristic
32C2×C3×C5×Q16C2211yescharacteristic
33C3×C5×C22⋊Q8C2211yescharacteristic
34C3×#4092C2211yescharacteristic
35C2×C3×#689C2211yescharacteristic
36C2×C3×#689C2211yescharacteristic
37C2×C3×#689C2211yescharacteristic
38C2×C3×#688C2211yescharacteristic
39C3×#4070C2211yescharacteristic
40C3×#4064—24no—
41C3×D5×Q16—24no—
42C2×C3×Dic20C2211yescharacteristic
43C2×C3×#677C2211yescharacteristic
44C2×C3×#676C2211yescharacteristic
45C2×C3×C8×D5C2211yescharacteristic
46C3×#4043C2211yescharacteristic
47C3×#4040—21no—
48C3×#4038C2211yescharacteristic
49C3×#4034—21no—
50C3×#4031—21no—
51C3×#4029—21no—
52C3×C5×#103C2211yescharacteristic
53C3×C5×#103C2211yescharacteristic
54C3×C5×C22⋊C8C2211yescharacteristic
55C3×#3967C2211yescharacteristic
56C3×#3967C2211yescharacteristic
57C3×C22⋊#168C2211yescharacteristic
58C3×#3953C2211yescharacteristic
59C3×#3952C2211yescharacteristic
60C3×#3952C2211yescharacteristic
61C3×#3948C2211yescharacteristic
62C3×#3942C2211yescharacteristic
63C3×#3941C2211yescharacteristic
64C3×#3011—51nomaximal, Hall
65C2×#4147C2×C311yescharacteristic
66C2×#4064C2×C311yescharacteristic, complemented
67C2×D5×Q16C2×C311yescharacteristic, complemented
68#65962C2×C311yescharacteristic, complemented
69C5×#451C2×C311yescharacteristic, complemented
70#65517C2×C311yescharacteristic, complemented
71#65476C2×C311yescharacteristic, complemented
72#65475C2×C311yescharacteristic, complemented
73#65336C2×C311yescharacteristic, complemented
74#65099C2×C311yescharacteristic, complemented
75#65097C2×C311yescharacteristic, complemented
76#65093C2×C311yescharacteristic, complemented
77#65091C2×C311yescharacteristic, complemented
78#65022C2×C311yescharacteristic, complemented
79#65016C2×C311yescharacteristic, complemented
80C2×C3×C5×Q8—22no—
81C2×C3×C5×Q8—22no—
82C2×C3×C5×Q8—21no—
83C2×C3×C5×Q8C2311yescharacteristic
84C2×C3×C5×Q8C2311yescharacteristic
85C2×C3×C5×Q8C2311yescharacteristic
86C22×C3×C4×C5—21no—
87C22×C3×C4×C5C2311yescharacteristic
88C2×C3×C22⋊D5—21no—
89C2×C3×C22⋊D5D411yescharacteristic
90C2×C3×C22⋊D5D411yescharacteristic
91C3×#713—28no—
92C3×#713—22no—
93C3×#713—22no—
94C3×#713—22no—
95C3×#713D414yes—
96C3×Q8×D5—28no—
97C3×Q8×D5—22no—
98C3×Q8×D5—22no—
99C3×Q8×D5—22no—
100C3×Q8×D5—22no—
101C3×Q8×D5—22no—
102C3×Q8×D5D414yes—
103C3×#709—28no—
104C3×#709—28no—
105C3×#709—22no—
106C3×#709—22no—
107C3×#709—22no—
108C3×#709—22no—
109C2×C3×D20—21no—
110C2×C3×D20—21no—
111C2×C3×D20D411yescharacteristic
112C2×C3×D20C2311yescharacteristic
113C2×C3×C4×D5—21no—
114C2×C3×C4×D5—21no—
115C2×C3×C4×D5—21no—
116C2×C3×C4×D5—21no—
117C2×C3×C4×D5—21no—
118C2×C3×C4×D5—21no—
119C2×C3×C4×D5C2311yescharacteristic
120C2×C3×C4×D5C2311yescharacteristic
121C2×C3×Dic10—21no—
122C2×C3×Dic10—21no—
123C2×C3×Dic10—21no—
124C2×C3×Dic10D411yescharacteristic
125C2×C3×Dic10C2311yescharacteristic
126C2×C3×Dic10C2311yescharacteristic
127C3×C5×Q16—22no—
128C3×C5×Q16—22no—
129C2×C3×C5×C8C2311yescharacteristic
130C2×C3×C5×C8C2311yescharacteristic
131C3×C5×C4⋊C4—21no—
132C3×C5×C4⋊C4C2311yescharacteristic
133C3×C5×C22⋊C4—21no—
134C3×C22⋊Dic5—21no—
135C3×#689—22no—
136C3×#689—22no—
137C3×#689—22no—
138C3×#688—22no—
139C3×#685—21no—
140C3×#685—21no—
141C3×#685—21no—
142C3×C4⋊Dic5—21no—
143C3×C4⋊Dic5C2311yescharacteristic
144C3×#683—21no—
145C3×#683—21no—
146C3×C4×Dic5—21no—
147C2×C3×#168C2311yescharacteristic
148C2×C3×#168C2311yescharacteristic
149C3×Dic20—22no—
150C3×#677—22no—
151C3×#676—22no—
152C3×C8×D5—22no—
153C2×C3×2−1+4—51no—
154C2×C3×#137—51no—
155C22×C3×Q16—51no—
156C3×#536—51no—
157C3×#452—51no—
158C3×#452—51no—
159C3×#452—51no—
160C3×#452—51no—
161C3×#451—51no—
162C3×#451—51no—
163C3×#451—51no—
164C3×#451D511yescharacteristic, complemented
165C3×#419—51no—
166C3×#416—51no—
167C3×#408—51no—
168C22×C5×Q8C22×C311yescharacteristic
169#4147—24no—
170#4147—24no—
171C2×#713—21no—
172C2×#713C22×C311yescharacteristic
173C2×#713C22×C311yescharacteristic
174C2×Q8×D5—21no—
175C2×Q8×D5C22×C311yescharacteristic
176C2×Q8×D5C22×C311yescharacteristic
177C2×Q8×D5C22×C311yescharacteristic
178C2×#709—21no—
179C2×#709—21no—
180C2×#709C22×C311yescharacteristic
181C2×#709C22×C311yescharacteristic
182C2×C5×Q16C22×C311yescharacteristic
183C2×C5×Q16C22×C311yescharacteristic
184C5×C22⋊Q8C22×C311yescharacteristic
185#4092C22×C311yescharacteristic
186C2×#689C22×C311yescharacteristic
187C2×#689C22×C311yescharacteristic
188C2×#689C22×C311yescharacteristic
189C2×#688C22×C311yescharacteristic
190#4070C22×C311yescharacteristic
191#4064—24no—
192D5×Q16—24no—
193C2×Dic20C22×C311yescharacteristic
194C2×#677C22×C311yescharacteristic
195C2×#676C22×C311yescharacteristic
196C2×C8×D5C22×C311yescharacteristic
197#4043C22×C311yescharacteristic
198#4040—21no—
199#4038C22×C311yescharacteristic
200#4034—21no—
201#4031—21no—
202#4029—21no—
203C5×#103C22×C311yescharacteristic
204C5×#103C22×C311yescharacteristic
205C5×C22⋊C8C22×C311yescharacteristic
206#3967C22×C311yescharacteristic
207#3967C22×C311yescharacteristic
208C22⋊#168C22×C311yescharacteristic
209#3953C22×C311yescharacteristic
210#3952C22×C311yescharacteristic
211#3952C22×C311yescharacteristic
212#3948C22×C311yescharacteristic
213#3942C22×C311yescharacteristic
214#3941C22×C311yescharacteristic
215#3011—51noSylow
216C23×C3×C5C2×D411yescharacteristic
217C22×C3×D5—21no—
218C22×C3×D5C2×D411yescharacteristic
219C22×C3×D5C2×D411yescharacteristic
220C3×C5×Q8—24no—
221C3×C5×Q8—21no—
222C3×C5×Q8—21no—
223C3×C5×Q8—21no—
224C3×C5×Q8—21no—
225C3×C5×Q8C2×D412yes—
226C3×C5×Q8C2×D412yes—
227C2×C3×C4×C5—24no—
228C2×C3×C4×C5—21no—
229C2×C3×C4×C5—21no—
230C2×C3×C4×C5—21no—
231C2×C3×C4×C5—21no—
232C2×C3×C4×C5—21no—
233C2×C3×C4×C5—21no—
234C2×C3×C4×C5C2×D411yescharacteristic
235C2×C3×C4×C5C2411yescharacteristic
236C3×C22⋊D5—24no—
237C3×C22⋊D5—22no—
238C3×C22⋊D5—22no—
239C2×C3×Dic5—21no—
240C2×C3×Dic5—21no—
241C2×C3×Dic5—21no—
242C2×C3×Dic5C2×D411yescharacteristic
243C2×C3×Dic5C2×D411yescharacteristic
244C3×D20—24no—
245C3×D20—24no—
246C3×D20—22no—
247C3×D20—21no—
248C3×D20C2×D412yes—
249C3×C4×D5—24no—
250C3×C4×D5—24no—
251C3×C4×D5—24no—
252C3×C4×D5—24no—
253C3×C4×D5—21no—
254C3×C4×D5—21no—
255C3×C4×D5—24no—
256C3×C4×D5—42no—
257C3×C4×D5C2×D412yes—
258C3×C4×D5C2×D412yes—
259C3×Dic10—24no—
260C3×Dic10—21no—
261C3×Dic10—24no—
262C3×Dic10—22no—
263C3×Dic10—21no—
264C3×Dic10—21no—
265C3×Dic10—42no—
266C3×Dic10C2×D412yes—
267C3×C5×C8—21no—
268C3×C5×C8—21no—
269C3×#168—21no—
270C3×#168—21no—
271C3×2−1+4—104no—
272C3×2−1+4—104no—
273C2×C3×#41—51no—
274C2×C3×#41—51no—
275C2×C3×#41—51no—
276C2×C3×#41—51no—
277C2×C3×#41—101no—
278C2×C3×#41—101no—
279C2×C3×#41—101no—
280C22×C3×Q8—51no—
281C22×C3×Q8—51no—
282C22×C3×Q8—51no—
283C22×C3×Q8—101no—
284C22×C3×Q8C2×D511yescharacteristic
285C3×#137—104no—
286C2×C3×Q16—51no—
287C2×C3×Q16—51no—
288C2×C3×Q16—51no—
289C2×C3×Q16—51no—
290C2×C3×Q16—104no—
291C2×C3×Q16C2×D511yescharacteristic
292C2×C3×Q16C2×D511yescharacteristic
293C2×C3×SD16—51no—
294C2×C3×SD16—51no—
295C2×C3×M16—51no—
296C22×C3×C8—51no—
297C3×C4⋊Q8—101no—
298C3×#124—101no—
299C3×#123—101no—
300C3×#123—101no—
301C3×C22⋊Q8—51no—
302C3×C22⋊Q8—51no—
303C3×C22⋊Q8—51no—
304C3×C22⋊Q8C2×D511yescharacteristic
305C3×#117—51no—
306C3×#103—51no—
307C3×#103—51no—
308C3×#103—51no—
309C3×#103—51no—
310C3×#103C2×D511yescharacteristic
311C3×#103C2×D511yescharacteristic
312C3×#102—51no—
313C3×#102—51no—
314C3×C22⋊C8—51no—
315C3×C22⋊C8—51no—
316C3×C22⋊C8—51no—
317C3×C22⋊C8C2×D511yescharacteristic
318C2×C5×Q8—22no—
319C2×C5×Q8—22no—
320C2×C5×Q8—21no—
321C2×C5×Q8C23×C311yescharacteristic
322C2×C5×Q8C23×C311yescharacteristic
323C2×C5×Q8C23×C311yescharacteristic
324C22×C4×C5—21no—
325C22×C4×C5C23×C311yescharacteristic
326C2×C22⋊D5—21no—
327C2×C22⋊D5C3×D411yescharacteristic
328C2×C22⋊D5C3×D411yescharacteristic
329#713—28no—
330#713—22no—
331#713—22no—
332#713—22no—
333#713C3×D414yes—
334Q8×D5—28no—
335Q8×D5—22no—
336Q8×D5—22no—
337Q8×D5—22no—
338Q8×D5—22no—
339Q8×D5—22no—
340Q8×D5C3×D414yes—
341#709—28no—
342#709—28no—
343#709—22no—
344#709—22no—
345#709—22no—
346#709—22no—
347C2×D20—21no—
348C2×D20—21no—
349C2×D20C3×D411yescharacteristic
350C2×D20C23×C311yescharacteristic
351C2×C4×D5—21no—
352C2×C4×D5—21no—
353C2×C4×D5—21no—
354C2×C4×D5—21no—
355C2×C4×D5—21no—
356C2×C4×D5—21no—
357C2×C4×D5C23×C311yescharacteristic
358C2×C4×D5C23×C311yescharacteristic
359C2×Dic10—21no—
360C2×Dic10—21no—
361C2×Dic10—21no—
362C2×Dic10C3×D411yescharacteristic
363C2×Dic10C23×C311yescharacteristic
364C2×Dic10C23×C311yescharacteristic
365C5×Q16—22no—
366C5×Q16—22no—
367C2×C5×C8C23×C311yescharacteristic
368C2×C5×C8C23×C311yescharacteristic
369C5×C4⋊C4—21no—
370C5×C4⋊C4C23×C311yescharacteristic
371C5×C22⋊C4—21no—
372C22⋊Dic5—21no—
373#689—22no—
374#689—22no—
375#689—22no—
376#688—22no—
377#685—21no—
378#685—21no—
379#685—21no—
380C4⋊Dic5—21no—
381C4⋊Dic5C23×C311yescharacteristic
382#683—21no—
383#683—21no—
384C4×Dic5—21no—
385C2×#168C23×C311yescharacteristic
386C2×#168C23×C311yescharacteristic
387Dic20—22no—
388#677—22no—
389#676—22no—
390C8×D5—22no—
391C2×2−1+4—51no—
392C2×#137—51no—
393C22×Q16—51no—
394#536—51no—
395#452—51no—
396#452—51no—
397#452—51no—
398#452—51no—
399#451—51no—
400#451—51no—
401#451—51no—
402#451C3×D511yescharacteristic, complemented
403#419—51no—
404#416—51no—
405#408—51no—
406C22×C3×C5—21no—
407C22×C3×C5—21no—
408C22×C3×C5—21no—
409C22×C3×C5C22×D411yescharacteristic
410C2×C3×D5—21no—
411C2×C3×D5—21no—
412C2×C3×D5—21no—
413C2×C3×D5—22no—
414C2×C3×D5—21no—
415C2×C3×D5—21no—
416C2×C3×D5—41no—
417C2×C3×D5—41no—
418C2×C3×D5#12012yes—
419C3×C4×C5—22no—
420C3×C4×C5—22no—
421C3×C4×C5—21no—
422C3×C4×C5—41no—
423C3×C4×C5—41no—
424C3×C4×C5C22×D411yescharacteristic
425C3×C4×C5C22×D411yescharacteristic
426C3×Dic5—21no—
427C3×Dic5—22no—
428C3×Dic5—41no—
429C3×Dic5—41no—
430C3×Dic5#12012yes—
431C3×#41—54no—
432C3×#41—102no—
433C3×#41—102no—
434C3×#41—102no—
435C3×#41—102no—
436C3×#41—108no—
437C3×#41—108no—
438C3×#41—102no—
439C3×#41—102no—
440C3×#41—108no—
441C3×#41—102no—
442C2×C3×Q8—22no—
443C2×C3×Q8—22no—
444C2×C3×Q8—21no—
445C2×C3×Q8—51no—
446C2×C3×Q8—54no—
447C2×C3×Q8—51no—
448C2×C3×Q8—51no—
449C2×C3×Q8—101no—
450C2×C3×Q8—101no—
451C2×C3×Q8—101no—
452C2×C3×Q8—102no—
453C2×C3×Q8—102no—
454C2×C3×Q8—102no—
455C2×C3×Q8—102no—
456C2×C3×Q8—108no—
457C2×C3×Q8—102no—
458C2×C3×Q8C22×D511yescharacteristic
459C2×C3×Q8C22×D511yescharacteristic
460C2×C3×Q8C22×D511yescharacteristic
461C2×C3×D4—51no—
462C2×C3×D4—51no—
463C2×C3×D4—51no—
464C2×C3×D4—51no—
465C2×C3×D4—101no—
466C2×C3×D4—101no—
467C2×C3×D4—101no—
468C22×C3×C4—21no—
469C22×C3×C4—51no—
470C22×C3×C4—51no—
471C22×C3×C4—101no—
472C22×C3×C4—101no—
473C22×C3×C4—101no—
474C22×C3×C4—101no—
475C22×C3×C4—101no—
476C22×C3×C4—101no—
477C22×C3×C4C22×D511yescharacteristic
478C3×Q16—22no—
479C3×Q16—22no—
480C3×Q16—102no—
481C3×Q16—102no—
482C3×Q16—102no—
483C3×Q16—102no—
484C3×SD16—102no—
485C3×SD16—102no—
486C3×M16—102no—
487C2×C3×C8—51no—
488C2×C3×C8—51no—
489C2×C3×C8—102no—
490C2×C3×C8C22×D511yescharacteristic
491C2×C3×C8C22×D511yescharacteristic
492C3×C4⋊C4—21no—
493C3×C4⋊C4—51no—
494C3×C4⋊C4—101no—
495C3×C4⋊C4—101no—
496C3×C4⋊C4—101no—
497C3×C4⋊C4C22×D511yescharacteristic
498C3×C22⋊C4—21no—
499C3×C22⋊C4—101no—
500C3×C22⋊C4—101no—
501C3×C22⋊C4—101no—
502C3×C22⋊C4—101no—
503C3×C42—101no—
504C23×C5C2×C3×D411yescharacteristic
505C22×D5—21no—
506C22×D5C2×C3×D411yescharacteristic
507C22×D5C2×C3×D411yescharacteristic
508C5×Q8—24no—
509C5×Q8—21no—
510C5×Q8—21no—
511C5×Q8—21no—
512C5×Q8—21no—
513C5×Q8C2×C3×D412yes—
514C5×Q8C2×C3×D412yes—
515C2×C4×C5—24no—
516C2×C4×C5—21no—
517C2×C4×C5—21no—
518C2×C4×C5—21no—
519C2×C4×C5—21no—
520C2×C4×C5—21no—
521C2×C4×C5—21no—
522C2×C4×C5C2×C3×D411yescharacteristic
523C2×C4×C5C24×C311yescharacteristic
524C22⋊D5—24no—
525C22⋊D5—22no—
526C22⋊D5—22no—
527C2×Dic5—21no—
528C2×Dic5—21no—
529C2×Dic5—21no—
530C2×Dic5C2×C3×D411yescharacteristic
531C2×Dic5C2×C3×D411yescharacteristic
532D20—24no—
533D20—24no—
534D20—22no—
535D20—21no—
536D20C2×C3×D412yes—
537C4×D5—24no—
538C4×D5—24no—
539C4×D5—24no—
540C4×D5—24no—
541C4×D5—21no—
542C4×D5—21no—
543C4×D5—24no—
544C4×D5—42no—
545C4×D5C2×C3×D412yes—
546C4×D5C2×C3×D412yes—
547Dic10—24no—
548Dic10—21no—
549Dic10—24no—
550Dic10—22no—
551Dic10—21no—
552Dic10—21no—
553Dic10—42no—
554Dic10C2×C3×D412yes—
555C5×C8—21no—
556C5×C8—21no—
557#168—21no—
558#168—21no—
5592−1+4—104no—
5602−1+4—104no—
561C2×#41—51no—
562C2×#41—51no—
563C2×#41—51no—
564C2×#41—51no—
565C2×#41—101no—
566C2×#41—101no—
567C2×#41—101no—
568C22×Q8—51no—
569C22×Q8—51no—
570C22×Q8—51no—
571C22×Q8—101no—
572C22×Q8C2×C3×D511yescharacteristic
573#137—104no—
574C2×Q16—51no—
575C2×Q16—51no—
576C2×Q16—51no—
577C2×Q16—51no—
578C2×Q16—104no—
579C2×Q16C2×C3×D511yescharacteristic
580C2×Q16C2×C3×D511yescharacteristic
581C2×SD16—51no—
582C2×SD16—51no—
583C2×M16—51no—
584C22×C8—51no—
585C4⋊Q8—101no—
586#124—101no—
587#123—101no—
588#123—101no—
589C22⋊Q8—51no—
590C22⋊Q8—51no—
591C22⋊Q8—51no—
592C22⋊Q8C2×C3×D511yescharacteristic
593#117—51no—
594#103—51no—
595#103—51no—
596#103—51no—
597#103—51no—
598#103C2×C3×D511yescharacteristic
599#103C2×C3×D511yescharacteristic
600#102—51no—
601#102—51no—
602C22⋊C8—51no—
603C22⋊C8—51no—
604C22⋊C8—51no—
605C22⋊C8C2×C3×D511yescharacteristic
606C2×C3×C5—41no—
607C2×C3×C5C2×#12011yescharacteristic
608C2×C3×C5#57811yescharacteristic
609C2×C3×C5#57811yescharacteristic
610C3×D5—22no—
611C3×D5—41no—
612C3×D5—42no—
613C23×C3—51no—
614C23×C3—51no—
615C23×C3—101no—
616C23×C3D4×D511yescharacteristic
617C3×Q8—24no—
618C3×Q8—21no—
619C3×Q8—21no—
620C3×Q8—21no—
621C3×Q8—21no—
622C3×Q8—52no—
623C3×Q8—104no—
624C3×Q8—102no—
625C3×Q8—104no—
626C3×Q8—101no—
627C3×Q8—101no—
628C3×Q8—101no—
629C3×Q8—202no—
630C3×Q8D4×D512yes—
631C3×Q8D4×D512yes—
632C3×D4—52no—
633C3×D4—102no—
634C3×D4—104no—
635C3×D4—104no—
636C3×D4—102no—
637C3×D4—102no—
638C3×D4—104no—
639C3×D4—101no—
640C2×C3×C4—24no—
641C2×C3×C4—21no—
642C2×C3×C4—21no—
643C2×C3×C4—21no—
644C2×C3×C4—21no—
645C2×C3×C4—21no—
646C2×C3×C4—21no—
647C2×C3×C4—51no—
648C2×C3×C4—52no—
649C2×C3×C4—52no—
650C2×C3×C4—51no—
651C2×C3×C4—104no—
652C2×C3×C4—104no—
653C2×C3×C4—104no—
654C2×C3×C4—104no—
655C2×C3×C4—104no—
656C2×C3×C4—101no—
657C2×C3×C4—101no—
658C2×C3×C4—101no—
659C2×C3×C4—101no—
660C2×C3×C4—101no—
661C2×C3×C4—202no—
662C2×C3×C4D4×D511yescharacteristic
663C2×C3×C4C23×D511yescharacteristic
664C3×C8—21no—
665C3×C8—21no—
666C3×C8—101no—
667C3×C8—101no—
668C22×C5—21no—
669C22×C5—21no—
670C22×C5—21no—
671C22×C5C22×C3×D411yescharacteristic
672C2×D5—21no—
673C2×D5—21no—
674C2×D5—21no—
675C2×D5—21no—
676C2×D5—21no—
677C2×D5—22no—
678C2×D5—41no—
679C2×D5—41no—
680C2×D5C3×#12012yes—
681C4×C5—22no—
682C4×C5—22no—
683C4×C5—21no—
684C4×C5—41no—
685C4×C5—41no—
686C4×C5C22×C3×D411yescharacteristic
687C4×C5C22×C3×D411yescharacteristic
688Dic5—21no—
689Dic5—22no—
690Dic5—41no—
691Dic5—41no—
692Dic5C3×#12012yes—
693#41—54no—
694#41—102no—
695#41—102no—
696#41—102no—
697#41—102no—
698#41—108no—
699#41—108no—
700#41—102no—
701#41—102no—
702#41—108no—
703#41—102no—
704C2×Q8—22no—
705C2×Q8—22no—
706C2×Q8—21no—
707C2×Q8—51no—
708C2×Q8—54no—
709C2×Q8—51no—
710C2×Q8—51no—
711C2×Q8—101no—
712C2×Q8—101no—
713C2×Q8—101no—
714C2×Q8—102no—
715C2×Q8—102no—
716C2×Q8—102no—
717C2×Q8—102no—
718C2×Q8—108no—
719C2×Q8—102no—
720C2×Q8C22×C3×D511yescharacteristic
721C2×Q8C22×C3×D511yescharacteristic
722C2×Q8C22×C3×D511yescharacteristic
723C2×D4—51no—
724C2×D4—51no—
725C2×D4—51no—
726C2×D4—51no—
727C2×D4—101no—
728C2×D4—101no—
729C2×D4—101no—
730C22×C4—21no—
731C22×C4—51no—
732C22×C4—51no—
733C22×C4—101no—
734C22×C4—101no—
735C22×C4—101no—
736C22×C4—101no—
737C22×C4—101no—
738C22×C4—101no—
739C22×C4C22×C3×D511yescharacteristic
740Q16—22no—
741Q16—22no—
742Q16—102no—
743Q16—102no—
744Q16—102no—
745Q16—102no—
746SD16—102no—
747SD16—102no—
748M16—102no—
749C2×C8—51no—
750C2×C8—51no—
751C2×C8—102no—
752C2×C8C22×C3×D511yescharacteristic
753C2×C8C22×C3×D511yescharacteristic
754C4⋊C4—21no—
755C4⋊C4—51no—
756C4⋊C4—101no—
757C4⋊C4—101no—
758C4⋊C4—101no—
759C4⋊C4C22×C3×D511yescharacteristic
760C22⋊C4—21no—
761C22⋊C4—101no—
762C22⋊C4—101no—
763C22⋊C4—101no—
764C22⋊C4—101no—
765C42—101no—
766C3×C5#301111yescharacteristic, complemented, Hall
767C22×C3—21no—
768C22×C3—21no—
769C22×C3—21no—
770C22×C3—52no—
771C22×C3—101no—
772C22×C3—101no—
773C22×C3—101no—
774C22×C3—101no—
775C22×C3—102no—
776C22×C3—101no—
777C22×C3—201no—
778C22×C3—201no—
779C22×C3C2×D4×D511yescharacteristic
780C3×C4—22no—
781C3×C4—22no—
782C3×C4—21no—
783C3×C4—41no—
784C3×C4—41no—
785C3×C4—52no—
786C3×C4—101no—
787C3×C4—102no—
788C3×C4—201no—
789C3×C4—201no—
790C3×C4C2×D4×D511yescharacteristic
791C3×C4C2×D4×D511yescharacteristic
792C2×C5—41no—
793C2×C5C2×C3×#12011yescharacteristic
794C2×C5C3×#57811yescharacteristic
795C2×C5C3×#57811yescharacteristic
796D5—22no—
797D5—41no—
798D5—42no—
799C23—51no—
800C23—51no—
801C23—101no—
802C23C3×D4×D511yescharacteristic
803Q8—24no—
804Q8—21no—
805Q8—21no—
806Q8—21no—
807Q8—21no—
808Q8—52no—
809Q8—104no—
810Q8—102no—
811Q8—104no—
812Q8—101no—
813Q8—101no—
814Q8—101no—
815Q8—202no—
816Q8C3×D4×D512yes—
817Q8C3×D4×D512yes—
818D4—52no—
819D4—102no—
820D4—104no—
821D4—104no—
822D4—102no—
823D4—102no—
824D4—104no—
825D4—101no—
826C2×C4—24no—
827C2×C4—21no—
828C2×C4—21no—
829C2×C4—21no—
830C2×C4—21no—
831C2×C4—21no—
832C2×C4—21no—
833C2×C4—51no—
834C2×C4—52no—
835C2×C4—52no—
836C2×C4—51no—
837C2×C4—104no—
838C2×C4—104no—
839C2×C4—104no—
840C2×C4—104no—
841C2×C4—104no—
842C2×C4—101no—
843C2×C4—101no—
844C2×C4—101no—
845C2×C4—101no—
846C2×C4—101no—
847C2×C4—202no—
848C2×C4C3×D4×D511yescharacteristic
849C2×C4C23×C3×D511yescharacteristic
850C8—21no—
851C8—21no—
852C8—101no—
853C8—101no—
854C2×C3—41no—
855C2×C3—102no—
856C2×C3—201no—
857C2×C3—202no—
858C2×C3D5×#12011yescharacteristic
859C2×C3#6610011yescharacteristic
860C2×C3#6611311yescharacteristic
861C5C3×#301111yescharacteristic, complemented, Sylow
862C22—21no—
863C22—21no—
864C22—21no—
865C22—52no—
866C22—101no—
867C22—101no—
868C22—101no—
869C22—101no—
870C22—102no—
871C22—101no—
872C22—201no—
873C22—201no—
874C22C2×C3×D4×D511yescharacteristic
875C4—22no—
876C4—22no—
877C4—21no—
878C4—41no—
879C4—41no—
880C4—52no—
881C4—101no—
882C4—102no—
883C4—201no—
884C4—201no—
885C4C2×C3×D4×D511yescharacteristic
886C4C2×C3×D4×D511yescharacteristic
887C3#1061191611yescharacteristic, direct product factor, Sylow
888C2—41no—
889C2—102no—
890C2—201no—
891C2—202no—
892C2C3×D5×#12011yescharacteristic
893C2C3×#6610011yescharacteristic
894C2C3×#6611311yescharacteristic
subgroupG/H
centerC22×C3C2×D4×D5
commutator, cosocleC2×C4×C5C24×C3
FrattiniC2×C4C23×C3×D5
FittingC3×C5×#451C2
socleC22×C3×C5C22×D4
prime radicalC2×C3×#4147C2
hypercenterC3×#451D5
hypocenterC5C3×#3011
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#451

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×C3×#4064C2semidirect
3. C2×C3×D5×Q16C2semidirect
4. C3×#65962C2semidirect
5. C3×C5×#451C2semidirect
6. C3×#65517C2semidirect
7. C3×#65476C2semidirect
8. C3×#65475C2semidirect
9. C3×#65336C2semidirect
10. C3×#65099C2semidirect
11. C3×#65097C2semidirect
12. C3×#65093C2semidirect
13. C3×#65091C2semidirect
14. C3×#65022C2semidirect
15. C3×#65016C2semidirect
16. #10611916C3direct (N × H)
66. C2×#4064C2×C3semidirect
67. C2×D5×Q16C2×C3semidirect
68. #65962C2×C3semidirect
69. C5×#451C2×C3semidirect
70. #65517C2×C3semidirect
71. #65476C2×C3semidirect
72. #65475C2×C3semidirect
73. #65336C2×C3semidirect
74. #65099C2×C3semidirect
75. #65097C2×C3semidirect
76. #65093C2×C3semidirect
77. #65091C2×C3semidirect
78. #65022C2×C3semidirect
79. #65016C2×C3semidirect
164. C3×#451D5semidirect
402. #451C3×D5semidirect
766. C3×C5#3011semidirect
861. C5C3×#3011semidirect
887. C3#10611916direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×C3×#41472
C2×C3×#40642
C2×C3×D5×Q162
C3×#659622
C3×C5×#4512
C3×#655172
C3×#654762
C3×#654752
C3×#653362
C3×#650992
C3×#650972
C3×#650932
C3×#650912
C3×#650222
C3×#650162
#106119163
C3×#30115